A-Life

Artificial life
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The late John von Neumann once pointed out that, in the past, Science has dealt mainly with problems of energy, power, force and motion. He predicted that in the future science would be much more concerned with problems of control, programming, information processing, organization, and systems. General purpose digital computers provide an excellent opportunity for studies of this kind, and von Neumann started a theory of automata based on them. He wished this theory to deal with the control, informational, and logical aspects of both man-made automata (such as digital and analog computers) and non-man-made systems (such as cells, nervous systems, and brains). Von Neumann's conception of automata theory was close to Wiener's conception of cybernetics. But von Neumann's automata theory was more about logic and digital computers, while Wiener's cybernetics was oriented more around physiology and control engineering.

One problem von Neumann posed and essentially solved was: What kind of logical organization is sufficient for an automaton to control itself in such a manner 
that it reproduces itself?

A cellular automaton is a theoretical machine that consists of elements called cells. Each cell has a value, or state, and is connected to certain neighboring cells so that they form a one- or multidimensional lattice. The states of the cells change at discrete time-steps. The new state of a cell is computed from the previous states of the connected neighboring cells using predefined rules. In Theory of Self-Reproducing Automata, von Neumann described a cellular automaton with twenty-nine possible states for each cell and in which every cell is connected to the cell above, below, left, and right (called a “von Neumann” neighborhood). He proved that the dynamics exhibited by such a cellular automaton are similar to the biological processes involved in self-reproduction and evolution.

John von Neumann and the history of DNA and self-replication
> Brenner : https://www.youtube.com/watch?v=5Ictxz1XCiY

Cellular Automaton [Mathworld]

https://mathworld.wolfram.com/Rule30.html

https://golly.sourceforge.io/

supports von Neumann's CA along with the Game of Life, and other rulesets.
open source, cross-platform application for exploring Conway's Game of Life 
and many other types of cellular automata. 


Golly-4.2-win-64bit
https://playgameoflife.com/

In late 1940, John von Neumann defined life as a being or organism which can reproduce itself and simulate a Turing machine.
Von Neumann was thinking about an engineering solution which would use electromagnetic components floating randomly in liquid or gas. This turned out not to be realistic with the technology available at the time. Stanisław Ulam invented cellular automata, which were intended to simulate von Neumann's theoretical electromagnetic constructions. Ulam discussed using computers to simulate his cellular automata in a two-dimensional lattice in several papers. In parallel, von Neumann attempted to construct Ulam's cellular automaton. Although successful, he was busy with other projects and left some details unfinished. His construction was complicated because it tried to simulate his own engineering design.
[ Picture | Stanisław Ulam, Richard Feynmann, John Von Neumann]
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John Conway began doing experiments in 1968 with a variety of different two-dimensional cellular automaton rules. Conway's initial goal was to define an interesting and unpredictable cell automaton. For example, he wanted some configurations to last for a long time before dying and other configurations to go on forever without allowing cycles. It was a significant challenge and an open problem for years before experts on cellular automata managed to prove that, indeed, the Game of Life admitted of a configuration which was alive in the sense of satisfying von Neumann's two general requirements. While the definitions before the Game of Life were proof-oriented, Conway's construction aimed at simplicity without a priori providing proof the automaton was alive.

  

[Game of Life , 1970]
Life is a binary () totalistic cellular automaton 
with a Moore neighborhood of range 

Conway chose his rules carefully, after considerable experimentation, to meet these criteria:

There should be no explosive growth.
There should exist small initial patterns with chaotic, unpredictable outcomes.
There should be potential for von Neumann universal constructors.
The rules should be as simple as possible, whilst adhering to the above constraints.
The game made its first public appearance in the October 1970 issue of Scientific American, in Martin Gardner's "Mathematical Games" column. Theoretically, the Game of Life has the power of a universal Turing machine: anything that can be computed algorithmically can be computed within the Game of Life. 

Inventing Game of Life (John Conway)



Life in Life

SmoothLife by Stephan Rafler

A generalization of Conway's "Game of Life" to a continuous domain
https://arxiv.org/abs/1111.1567
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vidi : https://www.youtube.com/watch?v=KJe9H6qS82I
Download Ready (26Mb)
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Lenia Portal : https://chakazul.github.io/lenia.html

A Work of independent researcher Bert Chan
Lenia is a system of continuous cellular automata *using Real Numbers* , a form of artificial life.
It was derived from Conway's Game of Life by making everything smooth, continuous and generalized.

Bert Chan's home

Lenia - Mathematical Life Forms.
https://www.youtube.com/watch?v=iE46jKYcI4Y



Paper: https://arxiv.org/abs/1812.05433
Code: https://github.com/Chakazul/Lenia
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https://www.youtube.com/watch?v=mSy4z8nDLno

 https://www.youtube.com/watch?v=AP3zeHyWakw

Particle Lenia and the energy-based formulation
https://google-research.github.io/self-organising-systems/particle-lenia/

demo : https://znah.net/lenia/